Table of Contents Author Guidelines Submit a Manuscript
Journal of Chemistry
Volume 2015, Article ID 986402, 10 pages
http://dx.doi.org/10.1155/2015/986402
Research Article

Unbiased Diffusion through a Linear Porous Media with Periodic Entropy Barriers: A Tube Formed by Contacting Ellipses

Universidad Autónoma Metropolitana Iztapalapa, Avenue San Rafael Atlixco 186, 09340 México, DF, Mexico

Received 18 February 2015; Accepted 26 May 2015

Academic Editor: Demeter Tzeli

Copyright © 2015 Yoshua Chávez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. S. Burada, Entropic Transport in Confined Media, Universität Augsburg, Augsburg, Germany, 2008.
  2. P. S. Burada, P. Hänggi, F. Marchesoni, G. Schmid, and P. Talkner, “Diffusion in confined geometries,” ChemPhysChem, vol. 10, no. 1, pp. 45–54, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. P. S. Burada, G. Schmid, and P. Hänggi, “Entropic transport: a test bed for the Fick-Jacobs approximation,” Philosophical Transactions of the Royal Society of London Series A: Mathematical, Physical & Engineering Sciences, vol. 367, no. 1901, pp. 3157–3171, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. P. S. Burada, G. Schmid, P. Talkner, P. Hänggi, D. Reguera, and J. M. Rubí, “Entropic particle transport in periodic channels,” BioSystems, vol. 93, no. 1-2, pp. 16–22, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. P. Malgaretti, I. Pagonabarraga, and J. M. Rubi, “Entropic transport in confined media: a challenge for computational studies in biological and soft-matter systems,” Frontiers in Physics, vol. 1, article 23, 2013. View at Publisher · View at Google Scholar
  6. L. Karwacki, M. H. F. Kox, D. A. M. de Winter et al., “Morphology-dependent zeolite intergrowth structures leading to distinct internal and outer-surface molecular diffusion barriers,” Nature Materials, vol. 8, no. 12, pp. 959–965, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. R. Haul, “J. Kärger, D. M. Ruthven: Diffusion in Zeolites and other Microporous Solids, J. Wiley & Sons INC, New York 1992. ISBN 0-471-50907-8. 605 Seiten, Preis: £ 117,” Berichte der Bunsengesellschaft für Physikalische Chemie, vol. 97, no. 1, pp. 146–147, 1993. View at Publisher · View at Google Scholar
  8. A. Berezhkovskii and G. Hummer, “Single-file transport of water molecules through a carbon nanotube,” Physical Review Letters, vol. 89, no. 6, Article ID 064503, 2002. View at Google Scholar · View at Scopus
  9. M. Gershow and J. A. Golovchenko, “Recapturing and trapping single molecules with a solid-state nanopore,” Nature Nanotechnology, vol. 2, no. 12, pp. 775–779, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. I. D. Kosińska, I. Goychuk, M. Kostur, G. Schmid, and P. Hänggi, “Rectification in synthetic conical nanopores: a one-dimensional Poisson-Nernst-Planck model,” Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, vol. 77, no. 3, Article ID 031131, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. L. T. Sexton, L. P. Horne, S. A. Sherrill, G. W. Bishop, L. A. Baker, and C. R. Martin, “Resistive-pulse studies of proteins and protein/antibody complexes using a conical nanotube sensor,” Journal of the American Chemical Society, vol. 129, no. 43, pp. 13144–13152, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Howorka and Z. Siwy, “Nanopore analytics: sensing of single molecules,” Chemical Society Reviews, vol. 38, no. 8, pp. 2360–2384, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. B. Hille, Ion Channels of Excitable Membranes, Sinauer Associates Inc., Sunderland, Mass, USA, 3rd edition, 2001.
  14. S. W. Cowan, T. Schirmer, G. Rummel et al., “Crystal structures explain functional properties of two E. coli porins,” Nature, vol. 358, no. 6389, pp. 727–733, 1992. View at Publisher · View at Google Scholar · View at Scopus
  15. L. Song, M. R. Hobaugh, C. Shustak, S. Cheley, H. Bayley, and J. E. Gouaux, “Structure of staphylococcal α-hemolysin, a heptameric transmembrane pore,” Science, vol. 274, no. 5294, pp. 1859–1865, 1996. View at Publisher · View at Google Scholar · View at Scopus
  16. R. Zwanzig, “Diffusion past an entropy barrier,” Journal of Physical Chemistry, vol. 96, no. 10, pp. 3926–3930, 1992. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Reguera and J. M. Rubí, “Kinetic equations for diffusion in the presence of entropic barriers,” Physical Review E, vol. 64, no. 6, Article ID 061106, 2001. View at Publisher · View at Google Scholar · View at Scopus
  18. A. M. Berezhkovskii, M. A. Pustovoit, and S. M. Bezrukov, “Diffusion in a tube of varying cross section: numerical study of reduction to effective one-dimensional description,” The Journal of Chemical Physics, vol. 126, no. 13, Article ID 134706, 2007. View at Publisher · View at Google Scholar · View at Scopus
  19. M. V. Vázquez, A. M. Berezhkovskii, and L. Dagdug, “Diffusion in linear porous media with periodic entropy barriers: a tube formed by contacting spheres,” Journal of Chemical Physics, vol. 129, no. 4, Article ID 046101, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. M.-V. Vázquez and L. Dagdug, “Numerical study assessing the applicability of the reduction to effective one-dimensional description of diffusion in a hemispherical shaped tube,” Journal of Non-Newtonian Fluid Mechanics, vol. 165, no. 17-18, pp. 987–991, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. M.-V. Vazquez and L. Dagdug, “Unbiased diffusion to escape through small windows: assessing the applicability of the reduction to effective one-dimension description in a spherical cavity,” Journal of Modern Physics, vol. 2, no. 4, pp. 284–288, 2011. View at Publisher · View at Google Scholar
  22. Y. Chávez, G. Chacón-Acosta, M. Vázquez, and L. Dagdug, “Unbiased diffusion to escape complex geometries: is reduction to effective one-dimensional description adequate to assess narrow escape times?” Applied Mathematics, vol. 5, no. 8, pp. 1218–1225, 2014. View at Publisher · View at Google Scholar
  23. P. Kalinay and J. K. Percus, “Projection of two-dimensional diffusion in a narrow channel onto the longitudinal dimension,” Journal of Chemical Physics, vol. 122, no. 20, Article ID 204701, 2005. View at Publisher · View at Google Scholar · View at Scopus
  24. P. Kalinay and J. K. Percus, “Corrections to the Fick-Jacobs equation,” Physical Review E, vol. 74, no. 4, Article ID 041203, 6 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  25. L. Dagdug and I. Pineda, “Projection of two-dimensional diffusion in a curved midline and narrow varying width channel onto the longitudinal dimension,” Journal of Chemical Physics, vol. 137, no. 2, Article ID 024107, 2012. View at Publisher · View at Google Scholar · View at Scopus
  26. S. Redner, A Guide to First-Passage Processes, Cambridge University Press, Cambridge, UK, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  27. M. Coppey, O. Bénichou, R. Voituriez, and M. Moreau, “Kinetics of target site localization of a protein on DNA: a stochastic approach,” Biophysical Journal, vol. 87, no. 3, pp. 1640–1649, 2004. View at Publisher · View at Google Scholar · View at Scopus
  28. P. Hanggi, P. Talkner, and M. Borkovec, “Reaction-rate theory: fifty years after Kramers,” Reviews of Modern Physics, vol. 62, no. 2, pp. 251–341, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. O. Bénichou, M. Coppey, M. Moreau, P.-H. Suet, and R. Voituriez, “Optimal search strategies for hidden targets,” Physical Review Letters, vol. 94, no. 19, Article ID 198101, 2005. View at Publisher · View at Google Scholar · View at Scopus
  30. D. Holcman and Z. Schuss, “Escape through a small opening: receptor trafficking in a synaptic membrane,” Journal of Statistical Physics, vol. 117, no. 5-6, pp. 975–1014, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  31. O. Bénichou and R. Voituriez, “Narrow-escape time problem: time needed for a particle to exit a confining domain through a small window,” Physical Review Letters, vol. 100, no. 16, Article ID 168105, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. Z. Schuss, A. Singer, and D. Holcman, “The narrow escape problem for diffusion in cellular microdomains,” Proceedings of the National Academy of Sciences of the United States of America, vol. 104, no. 41, pp. 16098–16103, 2007. View at Publisher · View at Google Scholar · View at Scopus
  33. E. Lippmaa, M. Mägi, A. Samoson, M. Tarmak, and G. Engelhardt, “Investigation of the structure of zeolites by solid-state high-resolution 29Si NMR spectroscopy,” Journal of the American Chemical Society, vol. 103, no. 17, pp. 4992–4996, 1981. View at Google Scholar · View at Scopus
  34. P. Chen, J. Gu, E. Brandin, Y.-R. Kim, Q. Wang, and D. Branton, “Probing single DNA molecule transport using fabricated nanopores,” Nano Letters, vol. 4, no. 11, pp. 2293–2298, 2004. View at Publisher · View at Google Scholar · View at Scopus
  35. R. Zwanzig, “Effective diffusion coefficient for a Brownian particle in a two-dimensional periodic channel,” Physica A: Statistical Mechanics and its Applications, vol. 117, no. 1, pp. 277–280, 1983. View at Google Scholar · View at Scopus
  36. S. Lifson and J. L. Jackson, “On the self-diffusion of ions in a polyelectrolyte solution,” The Journal of Chemical Physics, vol. 36, no. 9, pp. 2410–2414, 1962. View at Google Scholar · View at Scopus
  37. L. Dagdug, M.-V. Vazquez, A. M. Berezhkovskii, and S. M. Bezrukov, “Unbiased diffusion in tubes with corrugated walls,” Journal of Chemical Physics, vol. 133, no. 3, Article ID 034707, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. I. Pineda, M.-V. Vazquez, A. M. Berezhkovskii, and L. Dagdug, “Diffusion in periodic two-dimensional channels formed by overlapping circles: comparison of analytical and numerical results,” Journal of Chemical Physics, vol. 135, no. 22, Article ID 224101, 2011. View at Publisher · View at Google Scholar · View at Scopus
  39. A. M. Berezhkovskii and G. H. Weiss, “Propagators and related descriptors for non-Markovian asymmetric random walks with and without boundaries,” The Journal of Chemical Physics, vol. 128, Article ID 044914, 2008. View at Publisher · View at Google Scholar